A Base Station (BS) transmits information to mobile receivers through physical channels, in a zone around the BS called cell. All BS are asynchronous with each other. When a mobile station (MS) is switched on, it tries to get information from one BS, and thus needs to get synchronized to one BS. This operation is called initial cell search, or synchronization, or even initial acquisition of the synchronization code.
A physical channel typically consists of a layered structure of frames and time slots. Time slots are units containing chips and are part of a larger structure called frame. The primary synchronization channel (PSCH) is mapped into a physical channel. Said PSCH consists of a modulated synchronization code, which is transmitted once at the beginning of every slot in a frame from the BS to the MS. The MS receives the synchronization code within a sequence of data, which also comprises noise due to the transmission channel. This noise is mainly due to signals belonging to other physical channels, or to signals being transmitted by other BS.
The first step of synchronization, called slot search, is to acquire the slot timing. In order to acquire slot timing, it is suggested in the specifications 3G TS 25.214 V3.1.1 page 38, edited by the 3GPP group (3rd Generation Partnership Project), to make a total correlation between, on the one hand, a synchronization code locally generated by the MS, and, on the other hand, the sequence of data received by the MS, which comprises the synchronization code sent by the base station. The resulting correlation signal comprises in particular a correlation peak when the 2 codes are in synchronization, and a noise peak if the noise power is too high. The maximum of the correlation peaks found then determines the slot timing searched for.
All physical channels are transmitted at a particular carrier frequency. Both the BS and the MS use a local oscillator to modulate or demodulate the transmitted information. Whereas the local oscillator of the BS has an almost fixed frequency F of accuracy within +−0.1 ppm, the local oscillator of the MS can have a frequency F′ of accuracy within +−15 ppm in order to reduce cost of said MS. In an UMTS application, the physical channel has a carrier frequency of 2 GHz. This implies a high frequency offset up to +−30 KHz between frequency F and frequency F′, frequency F′ being higher or lower than F. Said high frequency offset degrades the computed correlation signal, as it implies an amplitude decrease of the correlation peak when codes are in phase. Therefore the maximum of the correlation signal could correspond to a noise peak, giving a wrong slot timing. Moreover, at some particular frequency offsets, the desired correlation peak is suppressed, so synchronization becomes impossible. More generally, beyond a particular high frequency offset, synchronization becomes very difficult. Therefore, the use of the classical correlator is restricted to frequency offsets accurring within a frequency bandwidth of +−7.5 KHz, in order to enable synchronization in a reduced time.